Question

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Find the value of the following expression:

(38 ⋅ 2−5 ⋅ 90)−2 ⋅ 2 to the power of negative 2 over 3 to the power of 3, whole to the power of 4 ⋅ 328 (5 points)

Write your answer in simplified form. Show all of your steps. (5 points)

Answer 1

Answer: 4

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Work Shown:

Part 1

`\left(3^8*2^(-5)*9^0\right)^(-2)*\left((2^(-2))/(3^3)\right)^4*3^(28)\\\\\\\left(3^8*(1)/(2^5)*1\right)^(-2)*\left((1)/(3^3)(1)/(2^2)\right)^4*3^(28)\\\\\\\left((3^8)/(2^5)\right)^(-2)*\left((1)/(3^3*2^2)\right)^4*3^(28)\\\\\\\left((2^5)/(3^8)\right)^(2)*\left((1)/(3^3*2^2)\right)^4*3^(28)\\\\\\(\left(2^5\right)^2)/(\left(3^8\right)^(2))*(1)/(\left(3^3\right)^4*\left(2^2\right)^4)*3^(28)\\\\\\(2^(5*2))/(3^(8*2))*(1)/(3^(3*4)*2^(2*4))*3^(28)\\\\\\`

Part 2

`(2^(10))/(3^(16))*(1)/(3^(12)*2^(8))*3^(28)\\\\\\(2^(10)*3^(28))/(3^(16)*3^(12)*2^(8))\\\\\\(2^(10)*3^(28))/(3^(16+12)*2^(8))\\\\\\(2^(10)*3^(28))/(3^(28)*2^(8))\\\\\\(2^(10))/(2^(8))\\\\\\2^(10-8)\\\\\\2^2\\\\\\4\\\\\\`

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The exponent rules I used were

• a^(-b) = 1/(a^b)
• (a/b)^(-c) = (b/a)^c
• a^b*a^c = a^(b+c)
• (a^b)/(a^c) = a^(b-c)
• (a^b)^c = a^(b*c)